An excited He+ ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm, in making a transition to ground state. The quantum number n, corresponding to its initial excited state is (for photon of wavelength λ, energy E =(1240eV/λ(in nm))

Question

An excited He+ ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm, in making a transition to ground state. The quantum number n, corresponding to its initial excited state is (for photon of wavelength λ, energy E =(1240eV/λ(in nm)) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

E = E1 +E2 13.6 (z2/n2) = (1240/λ1) +(1240/λ2) or (13.6(2)2/n2) = 1240 ((1/108.5) +(1/30.4))×(1/10-9) On solving, n = 5

Q. An excited $H e^{+}$ ion emits two photons in succession, with wavelengths $108.5$ nm and $30.4$ nm, in making a transition to ground state. The quantum number $n$ , corresponding to its initial excited state is (for photon of wavelength $λ$ , energy $E = \frac{1240 e V}{λ ( in nm )}$

$E = E_{1} + E_{2}$
$13.6 \frac{z ^{2}}{n ^{2}} = \frac{1240}{λ _{1}} + \frac{1240}{λ _{2}}$
or $\frac{13.6 ( 2 ) ^{2}}{n ^{2}} = 1240$
$(\frac{1}{108.5} + \frac{1}{30.4}) \times \frac{1}{1 0 ^{- 9}}$
On solving, $n = 5$

Q. An excited He+ ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm, in making a transition to ground state. The quantum number n, corresponding to its initial excited state is (for photon of wavelength λ, energy E=λ(innm)1240eV​

E=E1​+E2​ 13.6n2z2​=λ1​1240​+λ2​1240​ or n213.6(2)2​=1240 (108.51​+30.41​)×10−91​ On solving, n=5

Q. An excited $H e^{+}$ ion emits two photons in succession, with wavelengths $108.5$ nm and $30.4$ nm, in making a transition to ground state. The quantum number $n$ , corresponding to its initial excited state is (for photon of wavelength $λ$ , energy $E = \frac{1240 e V}{λ ( in nm )}$

$E = E_{1} + E_{2}$
$13.6 \frac{z ^{2}}{n ^{2}} = \frac{1240}{λ _{1}} + \frac{1240}{λ _{2}}$
or $\frac{13.6 ( 2 ) ^{2}}{n ^{2}} = 1240$
$(\frac{1}{108.5} + \frac{1}{30.4}) \times \frac{1}{1 0 ^{- 9}}$
On solving, $n = 5$